The Interplay of Fermi liquid theory and Luttinger's theorem in strongly correlated materials

Fermi liquid theory and Luttinger's theorem are two fundamental results in condensed matter physics which connect the degrees of freedom in the interacting system to those of the free Fermi gas. In the case of a Landau-Fermi liquid, the many-body physics and thermodynamics are described with the assistance of renormalized quasiparticles, while for systems where Luttinger's theorem is applicable the Fermi volume remains invariant with respect to interaction strength. While these two theorems are normally thought to go hand-in-hand, the underlying microscopic requirements for both are highly non-trivial, and require careful consideration. In this poster, I will explore and categorize both "Luttinger's theorem violating Fermi liquids" and "Luttinger's theorem preserving non-Fermi liquids", in addition to briefly discussing recent work on when both Luttinger's theorem and Fermi liquid theory remain applicable near an unconventional quantum critical point.